# -*- coding: utf-8 -*-

"""
created by 'palad' at

You have a number of envelopes with widths and heights given as a pair of integers (w, h).
One envelope can fit into another if and only if both the width and height of one envelope
is greater than the width and height of the other envelope.

What is the maximum number of envelopes can you Russian doll? (put one inside other)

Example:
Given envelopes = [[5,4],[6,4],[6,7],[2,3]], the maximum number of envelopes you can Russian doll is 3 ([2,3] => [5,4] => [6,7]).

最长递增子序列

F[i] = max{F[j]+1, j<i, A[j]<A[i]}


"""
import datetime

class Solution(object):
    def maxEnvelopes(self, envelopes):
        def bin_search(A, key):
            l, r = 0, len(A)
            while l < r:
                mid = (l + r) / 2
                if A[mid][1] < key[1]:
                    l = mid + 1
                else:
                    r = mid
            return l

        envelopes.sort(
            cmp=lambda x, y: x[0] - y[0] if x[0] != y[0] else y[1] - x[1])
        n = len(envelopes)
        tails = []
        for i in range(n):
            e = envelopes[i]
            p = bin_search(tails, e)
            if p == len(tails):
                tails.append(e)
            else:
                tails[p] = e
        return len(tails)

s = Solution()
startTime = datetime.datetime.now()
print s.maxEnvelopes([[5, 4], [6, 4], [6, 7], [2, 3]])
print('Time Cost: {}'.format(datetime.datetime.now()-startTime))

m = [[3419,8423],[164,2627],[3139,7517],[1751,4154],[9489,86],[6637,3814],[8056,4472],[1361,7808],[8951,7291],[2729,3128],[3981,8815],[492,3230],[8077,8257],[1046,8951],[7601,3995],[8077,2335],[7913,6100],[2120,552],[8052,7377],[3699,4314],[4956,9383],[1398,9645],[5612,3194],[1041,7969],[9353,9504],[3498,6074],[3778,6387],[6444,926],[8188,3068],[7573,9346],[1947,2744],[3161,1583],[6931,2466],[3123,2746],[3063,9465],[5436,4950],[2706,2321],[705,4817],[6848,3079],[7513,2377],[3314,3572],[1932,2535],[2635,6677],[31,1250],[3553,3075],[8978,2303],[6216,5277],[6544,5712],[8566,6145],[3541,9898],[7554,842],[1566,7443],[3891,2823],[8698,8532],[1692,6859],[4094,8342],[5207,9744],[3020,3461],[4752,6631],[2033,1323],[6094,3315],[16,8209],[3776,2627],[8889,2818],[755,2167],[9267,8809],[9701,777],[9464,9921],[2657,9329],[8606,8059],[6912,9454],[133,6606],[7149,5042],[7765,6180],[5361,4592],[7149,1438],[847,9109],[732,786],[9824,548],[9833,2443],[9920,232],[9957,8386],[1792,5312],[2950,3834],[3650,7948],[900,5644],[9741,7375],[964,6898],[7896,1036],[2274,3628],[5552,3985],[7669,8468],[5923,2191],[8154,1137],[7929,9618],[7960,4999],[3502,9719],[516,2896],[4059,2421],[3576,1295],[4835,20],[5679,8186],[7977,1570],[6570,8718],[5669,7159],[1610,6839],[5384,9486],[9839,1342],[5313,3512],[7560,7329],[3341,4860],[7253,8250],[4720,2680],[935,6817],[5006,9489],[3847,7892],[8131,367],[2769,8649],[7110,6644],[1890,5743],[1839,7297],[3431,1254],[5021,4290],[2902,1220],[4068,7124],[7223,1315],[5996,7738],[847,9773],[4553,7993],[3469,952],[3515,7868],[7258,8196],[9604,9484],[6500,397],[6891,2653],[495,4697],[3922,6202],[9333,956],[3946,3785],[1766,4052],[9708,5744],[7309,1019],[5938,3607],[1017,5011],[5151,6079],[4784,6132],[4469,8449],[8021,8735],[7943,2157],[5530,880],[2771,3653],[9851,776],[9714,7691],[4316,929],[9939,5982],[6155,3487],[4452,528],[6640,1633],[8847,3833],[8645,9925],[1031,4648],[6649,3067],[8969,2393],[3186,8448],[565,5104],[5092,1023],[7873,4665],[2515,5720],[6144,2960],[700,8342],[4431,4285],[7759,9179],[640,8724],[7558,6663],[2450,451],[5821,4868],[3596,760],[5009,6504],[4648,7689],[2385,4910],[7638,7327],[6783,5319],[3676,6987],[8202,5463],[101,9837],[9912,462],[2772,189],[8645,5511],[58,9865],[8230,7244],[7999,1685],[4491,6946],[2053,9514],[3479,7752],[8697,4200],[302,5464],[7360,1570],[7161,2012],[4755,304],[3088,1774],[6916,2967],[5635,1766],[4033,3320],[6795,3705],[4940,4164],[5895,2120],[8274,5160],[1587,2423],[9239,646],[5364,3424],[9598,1878],[4279,5057],[6076,4919],[5442,8463],[6785,2420],[8948,6061],[4613,3600],[5615,9879],[553,566],[3969,6767],[4233,8141],[5915,9627],[7497,9335],[2988,1508],[9533,5078],[1460,5468],[2030,6293],[5930,9963],[193,3541],[1911,2059],[295,6403],[9339,3504],[372,262],[4527,3135],[8408,1766],[2130,9366],[7508,1038],[3183,6667],[8439,4494],[3545,9626],[4932,1949],[7300,5433],[9733,3062],[9043,8371],[4449,1292],[3780,3665],[4830,6385],[1914,2260],[9547,8398],[8192,4081],[9069,38],[7308,4335],[4486,3126],[3224,6383],[6189,1328],[3401,935],[9071,2072],[4591,5583],[4437,8822],[4282,5162],[8733,3858],[2840,1896],[3480,3917],[6857,18],[2789,2228],[2912,7451],[2652,5706],[995,1861],[8674,6892],[9996,9738],[5449,8871],[8312,1103],[5457,4655],[2453,6727],[6094,433],[6805,443],[2448,525],[8633,7809],[628,2267],[720,2152],[4002,2141],[4648,7356],[7727,7373],[2672,7377],[2167,8724],[7647,2675],[5651,2636],[7644,744],[6601,4675],[3520,9348],[6569,3205],[9032,1994],[551,5461],[123,1252],[6170,4152],[1065,8283],[6624,5409],[7434,8864],[1182,6224],[3507,5842],[236,5240],[8487,6696],[2569,5827],[3541,7796],[2448,5561],[8487,646],[3523,9671],[1627,7796],[8190,7153],[5359,7583],[205,7545],[6987,4837],[5565,2428],[6259,9303],[9802,2069],[6574,167],[1302,1832],[278,3384],[568,7350],[8494,5624],[42,4217],[8344,3529],[3992,5501],[9033,4418],[9092,3589],[8016,1091],[9518,6786],[6403,7721],[8460,1063],[4757,6917],[4226,3967],[735,1858],[635,381],[7161,3228],[5017,3918],[4288,1162],[1260,981],[5776,8491],[9548,2987],[6748,2291],[5319,3510],[2631,9475],[4384,5186],[3357,5721],[7295,7478],[8801,943],[1418,3917],[689,6308],[1366,3676],[3710,7366],[6108,475],[5856,8197],[8403,2726],[5214,6996],[5813,7581],[2058,1726],[9845,687],[4647,2464],[6379,4875],[9739,557],[4093,9986],[3154,6687],[4032,1770],[4686,5511],[6607,1506],[5590,226],[8861,7951],[1146,1162],[7158,1662],[9817,1726],[6390,9393],[1549,1160],[5843,7524],[7125,24],[5006,1893],[3563,3810],[2964,7382],[2880,7801],[9028,8592],[8650,7525],[1611,7947],[8537,789],[6586,4676],[9236,7970],[5273,5041],[6595,3801],[2224,4833],[6583,8983],[4913,5398],[1634,1467],[5328,8075],[806,9955],[3891,568],[4013,9055],[7210,4487],[2670,2048],[4324,762],[250,5714],[4946,4326],[6442,4346],[8879,90],[4282,8913],[7466,8562],[9660,1411],[6163,529],[2526,5216],[7677,1516],[175,6919],[4090,7858],[86,2127],[2833,4769],[6810,2645],[2372,4302],[9570,8819],[480,4842],[2922,8848],[993,346],[9707,112],[4177,9837],[3737,1106],[186,6071],[3165,2657],[7210,7813],[3805,5090],[3419,7418],[354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3],[3808,6077],[781,3127],[9173,4590],[899,2995],[4051,954],[9243,8362],[8938,4409],[3188,1532],[2249,9040],[7114,9046],[1740,6885],[2615,2148],[1510,8926],[4227,1147],[5997,2262],[1417,2674],[3820,2181],[9098,9475],[3746,4257],[412,8446],[663,5744],[9555,9627],[2522,3780],[5947,9114],[3905,6085],[7480,6673],[5364,4484],[3534,7541],[968,8735],[4455,7256],[8060,6737],[8651,3807],[1934,3884],[7202,5283],[9484,7352],[5177,4357],[4339,6484],[5991,4335],[456,5618],[9346,5048],[2766,3914],[4255,6051],[5640,1250],[299,3902],[419,5563],[8955,4365],[983,3048],[4353,6883],[6841,9626],[1615,5270],[3982,5329],[6456,2163],[4364,9138],[1003,6413],[3814,3778],[7118,302],[9120,9990],[5451,3600],[8257,7596],[2273,613],[5073,3466],[7381,9964],[6522,626],[1703,7035],[3967,9030],[1257,161],[5552,3979],[1768,211],[2876,6536],[5140,3598],[8197,8480],[5479,8697],[2928,9199],[7212,3169],[7143,3001],[1733,1757],[6663,4713],[9800,2084],[3100,7889],[1689,7732],[33,415],[2662,1965],[3862,5443],[6117,8423],[6086,6061],[6982,5374],[4200,3990],[184,7966],[9176,5485],[5230,839],[2898,2825],[6314,8267],[3992,5052],[2786,444],[5479,2974],[4697,4700],[1346,3623],[4013,5423],[7598,2701],[3567,7535],[3707,8244],[9546,7458],[9561,1936],[71,4279],[7553,3781],[6582,6501],[9101,5686],[7841,8746],[8097,7361],[7935,8958],[7534,5240],[5585,8928],[4367,7079],[7324,4860],[9539,6018],[6668,9315],[5286,8980],[2940,1674],[1522,8413],[7845,2925],[1388,6138],[5562,3999],[1463,1996],[8985,9631],[9838,8286],[4245,5168],[7122,6256],[7841,4778],[4329,7476],[3768,8775],[1722,3121],[4898,1483],[6853,5591],[7183,7674],[6346,9785],[4274,9380],[6177,9055],[8734,8074],[2386,8483],[8394,6440],[2347,1067],[1010,9449],[2152,7005],[6250,6177],[4091,2994],[6632,147],[3185,950],[9597,9980],[6261,8930],[2619,5595],[4379,9916],[3261,9747],[2973,3377],[4921,9300],[285,6678],[2984,367],[6745,1742],[6239,4275],[9495,203],[2935,6366],[8851,2883],[7106,1716],[4738,702],[1292,793],[8056,6187],[9807,2960],[9481,9137],[1141,5908],[4995,4355],[3178,1167],[6955,8940],[1751,9817],[2890,1022],[6629,6746],[1466,2952],[6851,7434],[7705,337],[2538,2608],[2591,5529],[1665,5354],[1324,1050],[435,3335],[6052,4885],[4797,6596],[2321,740],[4653,5713],[9328,7872],[2636,6837],[9760,1831],[1483,5387],[5657,3689],[3836,4442],[1512,7359],[6820,1812],[2239,8105],[8444,5194],[6191,3604],[7474,9769],[9831,1850],[6549,4169],[1529,450],[1851,8757],[9459,2670],[7448,6432],[4959,4578],[3865,8954],[3812,1218],[4345,4546],[6053,6965],[3435,5784],[917,3418],[4237,1919],[4538,7969],[2044,9572],[9247,6492],[2786,3815],[2889,1597]]
startTime = datetime.datetime.now()
print s.maxEnvelopes(m)
print('Time Cost: {}'.format(datetime.datetime.now()-startTime))
